Rational systems and Matrix Inequalities to the multicriteria analysis of visual servos

Abstract

This paper outlines a generic method to the analysis of eye-in-hand position-based or image-based visual servos. Aside from convergence, the fulfillment of additional important criteria can be assessed, e.g. the target visibility, the avoidance of actuators' saturations, and the guarantee of 3D constraints. The field of nonlinear "rational" systems is first shown to constitute a sound and versatile framework to the problem. The fundamentals of a solution based on Lyapunov theory are overviewed next, together with the noteworthy difficulties raised by robotics. Constructive results are finally sketched out, in terms of a feasibility/optimization program subject to matrix inequalities. A case study illustrates the approach.